1. Chapter 11 Rotational Mechanics

2. Recall: If you want an object to move, you apply a FORCE.

3. Similarly, If you want an object to turn or rotate, you apply a TORQUE.

4. Forces produce motion. Torques produce rotation.

5. 11.1 Torque Torque is the force applied in a perpendicular fashion to an object in order to cause rotation.

6. 11.1 Torque Torque is the product of force and the lever arm. force X lever arm (N) ๋ (meters)

7. 11.1 Torque units: N ๋ meter (same units as work, except they are very different concepts)

8. 11.1 Torque Lever arm – the perpendicular distance between an axis and the line of action of a force that tends to produce rotation about an axis

9. 11.1 Torque Lever arm: The distance from the turning axis to the point of contact.

10. 11.2 Balanced Torques a pair of torques can balance each other

11. 11.2 Balanced Torques EX: seesaw 200 N 400 N equidistantunequal distances

12. 11.3 Torque and Center of Gravity Center of Gravity: the point located at the object’s average position of weight

13. 11.3 Torque and Center of Gravity Center of gravity has an effect on whether or not forces will produce rotation

14. 11.4 Rotational Inertia Recall: Inertia – resistance to change in motion There is inertia in rotation.

15. 11.4 Rotational Inertia rotational inertia – (also called moment of inertia) the resistance of an object to changes in its rotational motion

16. 11.4 Rotational Inertia dependent on two things: 1. mass 2. radial distance from axis

17. 11.4 Rotational Inertia A torque is needed to change rotational motion just as a force is needed to change linear motion.

18. 11.4 Rotational Inertia Remember that acceleration is constant regardless of mass. Therefore the acceleration of a rolling object is not dependent on the mass of the objects.

19. 11.4 Rotational Inertia The less mass an object has concentrated farthest from the center of gravity, the faster it will roll since its has less rotational inertia.

20. 11.5 Rotational Inertia and Gymnastics The human body has 3 principle axes of rotation.

21. 11.5 Rotational Inertia and Gymnastics 1. Longitudinal axis: from head to toe least amount of inertia EX: spinning

22. 11.5 Rotational Inertia and Gymnastics 2. Transverse axis: EX: flipping

23. 11.5 Rotational Inertia and Gymnastics 3. Median axis: EX: cartwheel

24. 11.6 Angular Momentum Recall: momentum is inertia of motion

25. 11.6 Angular Momentum angular momentum : inertia of rotational motion

26. 11.6 Angular Momentum product of rotational inertia and rotational velocity

27. 11.6 Angular Momentum angular momentum = inertia X rotational velocity or I ๋ 

28. 11.6 Angular Momentum Also, angular momentum = mvr Where m=mass v = velocity r = radius of circular path

29. 11.6 Angular Momentum r m v

30. Recall Newton’s First Law of Motion…

31. 11.6 Angular Momentum For angular momentum: “An object or system of object’s will maintain its angular momentum unless acted upon by an unbalanced external torque”

32. 11.7 Conservation of Angular Momentum Law of Conservation of Angular Momentum: “ If no unbalanced external torque acts on a rotating system, the angular momentum of that system is constant”